Get yourself a nice propane weed burner, burn them down, as soon as green shoots appear a week or two later hit them and the area with a healthy dose of Round-Up. In the spring till up the area then plant your hops

You don't need a preexisting condition, just a basic allergy to PI: when I was eight my dad was clearing out some back acreage and burning the brush he piled up. And I was playing in the smoke. I ended up in the hospital being pumped full of epinephrine for a few days.